A geometric approach to a generalized virial theorem

The virial theorem, introduced by Clausius in the field of statistical mechanics and later applied in both classical mechanics and quantum mechanics, is studied by making use of symplectic formalism as an approach, in the case of both the Hamiltonian and Lagrangian systems. The possibility of establ...

Full description

Saved in:
Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-10, Vol.45 (39), p.395210-19
Main Authors: Cariñena, José F, Falceto, Fernando, Rañada, Manuel F
Format: Article
Language:English
Subjects:
Analogies
canonical transformations
Classical mechanics
Exact sciences and technology
Formalism
Hamiltonian systems
Mathematical analysis
Physics
position dependent mass
Quantum mechanics
Statistical mechanics
symplectic manifolds
symplectic quantum mechanics
Theorems
Transformations
Virial theorem
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The virial theorem, introduced by Clausius in the field of statistical mechanics and later applied in both classical mechanics and quantum mechanics, is studied by making use of symplectic formalism as an approach, in the case of both the Hamiltonian and Lagrangian systems. The possibility of establishing virial-like theorems from one-parameter groups of non-strictly canonical transformations is analysed; the case of systems with a position-dependent mass is also discussed. Using the modern symplectic approach to quantum mechanics, we arrive at the quantum virial theorem in full analogy with the classical case.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/39/395210